$ = ( 1 - \dfrac{1}{4})( 1- \dfrac{1}{9})...(1-\dfrac{1}{10\ 000})$
$ = \dfrac{3}{4}. \dfrac{8}{9}. \dfrac{15}{16} . ....\dfrac{9\ 999}{10\ 000}$
$ = \dfrac{1*3}{2*2}. \dfrac{2*4}{3*3}. \dfrac{3*5}{4*4}..... \dfrac{99* 101}{100*100}$
$ = \dfrac{1*2*3*...*99}{2*3*4*...*100} . \dfrac{3*4*5*...*101}{2*3*4*...*100}$
$ = \dfrac{1}{100}. \dfrac{101}{2} = \dfrac{101}{200}$
